EE392m Fault Diagnostics Systems Introduction

Transcription

1 E39m Spring 9 EE39m Fault Diagnostics Systems Introduction Dimitry Consulting Professor Information Systems Laboratory 9 Fault Diagnostics Systems

2 Course Subject Engineering of fault diagnostics systems Embedded computer interacting with real world Detect abnormal operation Fault tolerance: more than 8% of critical control code Operations and maintenance More than 5% of the system lifetime costs Troubleshooting support Condition-based maintenance CBM 9 Fault Diagnostics Systems

3 Prerequisites and Course Place The subject is not covered in other courses Prerequisites (helpful but not necessary) Stat 6; EE63 or Eng 7a; EE78 or Eng 7b The course is about technical approaches that are actually used in fault diagnostics applications Survived demands of real life Used and supported by BS-level engineers in industry Should be accessible to a Stanford grad student 9 Fault Diagnostics Systems 3

4 Course Mechanics Class website: Weely seminars Follow website announcements Guest lecturers from diverse industries Co-sponsored by NASA Travel support for lecturers Lecture notes will be posted as available Attendance Reference texts Isermann; Chiang, Russel, & Braatz; Patton, Clar & Fran Different coverage Contact me if you have a specific interest 9 Fault Diagnostics Systems 4

5 On-line (Embedded) Functions Embedded system, anomaly warnings BIT Built-in-Test BITE Built-in-Test Equipment FDIR Fault Detection Identification and Recovery FT-RM Fault Tolerance and Redundancy Management 9 Fault Diagnostics Systems 5

6 Off-line Functions Reliability FMECA- Failure Mode, Effects, and Criticality Analysis Design time analysis open loop Maintenance and Support Diagnostics for maintenance Troubleshooting support Test equipment CBM Condition Based Maintenance Pre-testing dis drives 9 Fault Diagnostics Systems 6

7 Fault Diagnostics in Industry Space systems Defense systems: aviation, marine, and ground Commercial aerospace Aircraft, jet engines Ground vehicles Locomotives, trucs, cars High-tech Networs and IT systems Dis drives Server farms Process control IC Manufacturing Refineries Power plants Oil and gas drilling 9 Fault Diagnostics Systems 7

8 Guest Lecture Overview # Date Lector From Diagnostics Application 3-Mar-9 Stanford Introduction and overview 7-Apr-9 Rabover VMTurbo (EMC) Networs and IT systems 3 4-Apr-9 Tuv Intel IC Manufacturing processes 4 -Apr-9 Fele Honeywell Avionics of commercial aircraft 5 8-Apr-9 Adibhatla GE Infrastructure Jet engines 6 5-May-9 7 -May-9 Urmanov Sun Computing systems 8 9-May-9 Bodden Locheed Military aircraft systems 9 6-May-9 Kolmanovsy Ford Automotive powertrain -Jun-9 9 Fault Diagnostics Systems 8

9 Diagnostics Methods Overview Shewhart chart (Control chart) Multivariable SPC, T Model-based estimation Least squares estimation Integrated diagnostics Cascaded design 9 Fault Diagnostics Systems 9

10 Abnormality Detection - SPC SPC - Statistical Process Control monitoring of manufacturing processes warning for off-target quality Main SPC method Shewhart Chart (9s) Also see EWMA (94s) CuSum (95s) Western Electric Rules (95s) 9 Fault Diagnostics Systems

11 SPC: Shewhart Control Chart quality variable W.Shewhart, Bell Labs, 94 Statistical Process Control (SPC) UCL mean + 3 σ LCL mean - 3 σ sample Upper Control Limit mean Lower Control Limit Walter Shewhart (89-967) Fault Diagnostics Systems

12 Shewhart Chart, cont d Quality variable assumed randomly changing around a steady state value Detection: y(t) > UCLmean+3 σ For normal distribution, false alarm probability is less than.7% e( t) y( t) σ µ P(e > 3) -Φ(3).35 - P(e < 3) Φ(-3).35 - LCL UCL 9 Fault Diagnostics Systems

13 Shewhart Chart Hypothesis Test Null hypothesis given mean and covariance H : y( t) ~ N( µ, σ ) P ( H p ) Fault hypothesis a different mean H : y( t) ~ N( µ µ, σ ) P ( H p ) Hypothesis testing given Y y( t) find X { H, H } 9 Fault Diagnostics Systems 3

14 Bayesian Formulation Data: Y X Observation Underlying State Bayes rule P( X Y ) P( Y X ) P( X ) c P( Y X Observation model: Prior model: P(X ) Maximum A posteriori Probability estimate X ) ( log P( Y X ) log P( X )) arg min L log posterior index Rev. Thomas Bayes (7-76) 9 Fault Diagnostics Systems 4

15 Hypothesis Testing Null hypothesis log ( Y X ) ( y µ ) σ Fault hypothesis log ( Y X ) ( µ ) σ y Log-lielihood ratio P( H Y ) Λ log L L P( H Y ) Declare fault if Λ L L y µ log p σ y µ P log P( X ) log p P log P( X ) log p ( ) ( p ) > σ > log( p) p p p p.3 3σ 9 Fault Diagnostics Systems 5

16 Shewhart Chart: Use Examples SPC in manufacturing Fault monitoring Fault tolerance sensor integrity monitoring Sensor Reference + - y < 3σ no yes Fault Normal 9 Fault Diagnostics Systems 6

17 Diagnostics Methods Overview Shewhart chart (Control chart) Multivariable SPC, T Model-based estimation Least squares estimation Integrated diagnostics Cascaded design 9 Fault Diagnostics Systems 7

18 Multivariable SPC Chi-squared CDF Univariate process ( ) P z > c F( c,) µ z y ~ χ σ Φ( c) + Φ( c) Two independent univariate processes z 9 ( y ) ( ) µ y µ + ~ χ σ 3 z σ 3 z P ( ) z > c F( c ;) Fault Diagnostics Systems 8

19 Multivariable SPC Two correlated univariate processes y (t) and y (t) y cov(y,y ) Q, Q - L T L Uncorrelated linear combinations z(t) L [y(t)-µ] µ µ z µ T ( y µ ) Q ( y µ ) ~ χ Declare fault (anomaly) if ( ) T ( ) y µ Q y µ > c P ( ) z > c F( c ;) y y 9 Fault Diagnostics Systems 9

20 9 Fault Diagnostics Systems Multivariate SPC - Hotelling's T Empirical parameter estimates ( ) ( ) µ µ µ µ y t y t y n Q X E t y n T n t T n t cov ) ) ( )( ) ( ( ˆ ) ( ˆ Hotelling's T statistics is T can be trended as a univariate SPC variable ( ) ( ) µ µ ) ( ˆ ) ( t y Q t y T T Harold Hotelling ( )

21 Diagnostics Methods Overview Shewhart chart (Control chart) Multivariable SPC, T Model-based estimation Least squares estimation Integrated diagnostics Cascaded design 9 Fault Diagnostics Systems

22 Least Squares Estimation Linear observation model: Y CX + v Fault signature model Columns of C are fault signatures Could be obtained from physics model secant method Could be identified from data: regression, data mining Estimate regularized least squares Xˆ Carl Friedrich Gauss ( ) ( T ) T C C + ri C Y 9 Fault Diagnostics Systems

23 Bayesian Estimation Observation model: P(Y X) Prior models: P(X) MAP estimate: Xˆ Y CX + X arg min v ~ N (, R) Y CX Q log P( Y X ) v + ~ N (, Q) log P( X ) X R 3 log P( X ) T + X R X... Xˆ ( T C Q C R ) T + Q C Y 9 Fault Diagnostics Systems 3

24 Model-based Residuals Compute model-based prediction residual Y Y raw -f(u,x) If X (nominal case) we should have Y. Residuals Y reflect faults Sensor fault model - additive output change Actuator fault model - additive input change Plant Data Collected on-line Input data Output data input variables Plant Model output variables + - Fault Diagnostics prediction residual 9 Fault Diagnostics Systems 4

25 Example: Jet Engine Model Nonlinear jet engine model static map Residuals Linearized model 9 Y Y raw f ( U, X ) Turbine deterioration Y CX + v X Bleed band lea EGT sensor drift f ( U, X ) C X Fault Diagnostics Systems 5

26 Example: Fault Estimates Maintenance decision support tool Honeywell LF57 Engine Fleet Estimates of (fault) performance parameter deterioration 9 HP Spool Deterioration (%) Bleed Band Leaage (%) EGT Sensor Offset (deg C) Sample No Sample No Sample No. Ganguli, Deo, &, IEEE CCA 4 Fault Diagnostics Systems 6

27 Diagnostics Methods Overview Shewhart chart (Control chart) Multivariable SPC, T Model-based estimation Least squares estimation Integrated diagnostics Cascaded design 9 Fault Diagnostics Systems 7

28 Cascaded Design Increasing complexity and integration of system Slower time scale Simple inner loop models Examples Control systems Estimation and data fusion Fault diagnostics systems System Subsystem Unit Unit 9 Fault Diagnostics Systems 8

29 Integrated System Diagnostics Complex integrated systems Examples Aerospace vehicle, e.g. B777 Large scale computer networ Medical equipment Decision Support Interface Integrated Diagnostic System Subsystem Diagnostics Subsystem Diagnostics Subsystem n Diagnostics 9 Fault Diagnostics Systems 9

30 Discrete Fault Signatures Model of root cause fault : Y B Root Cause Symptom Code # Null # # #3 #4 #5 #6 # # #3 #4 #5 #6 #7 9 Fault Diagnostics Systems 3

31 Estimation Algorithm Diagnosis problem: Given data Y, diagnose root cause Solution: arg min Minimal Hamming distance Justifications Case-based reasoning (table of fault cases) Model-based reasoning (fault signature model) Bayesian Y B 9 Fault Diagnostics Systems 3

32 Bayesian Justification log P( Y Data Observation model P( y b H ) p 9 Y P( Y X H ) c ) X + w { H :, H : B,, H n } n : B K j j P( y b H ) p n log( y b j j log P( Y H ) log( p) + log p y j b j p y j b ) j n j y j Fault Diagnostics Systems 3 b j y j follows the model deviates from the model ( log p log( p )) >, for p < /

33 Bayesian Justification Prior model P (X ) P( H ) ( n + ) log P( H ) d MAP Estimate arg min arg min arg min ( log P( Y H ) log P( )) ( ) c + w y b + d y b H 9 Fault Diagnostics Systems 33

34 Conclusions Basic diagnostics estimation methods Are nown for long time Used in on-line systems for less time Can be explained in several ways, e.g., Bayesian Engineering of fault diagnostics systems Is new and current Will be discussed in guest lectures Not just diagnostics algorithms 9 Fault Diagnostics Systems 34

35 Guest Lectures: Approaches # Date Lector From Application Approach 7-Apr-9 Rabover EMC Networ Integrated diagnostics 3 4-Apr-9 Tuv Intel IC Manufacture Fault signature ID 4 -Apr-9 Fele Honeywell Aircraft Integrated diagnostics 5 8-Apr-9 Adibhatla GE Infra Jet Engines Multivariate estimation 7 -May-9 Urmanov Sun Computing Multivariate SPC, ML 8 9-May-9 Bodden Locheed Aircraft Fault tolerance 9 6-May-9 Kolmanovsy Ford Automotive Model-based 9 Fault Diagnostics Systems 35